Thursday, August 20, 2009

The Photoelectric Effect

You cover this topic in your first semester of Freshman chemistry. But at the time I have to say that I failed to grasp the weirdness (and pure scientific genius) of Einstein's nobel prize winning experiment dealing with the photoelectric effect. I don't pretend to be able to condense a good 50 years of scientific inquiry into one blog post, so I'm just going to focus on the single part of the photoelectric effect that I seriously missed in Freshman chem, and am only now beginning to grasp in Physical Chemistry.

The energy of an electron ejected from a metallic surface depends not on how much light is hitting said metallic surface, but rather how often the light hits the metallic surface. To illustrate this odd phenomena, suppose a ball being hit by another ball (in a perfectly elastic collision for ease of explanation):

Now, in mechanics (and if you're familiar with pool) we would expect the ball to hit the other ball, stop, and for the second ball to continue in motion, like so:

This would happen no matter how hard we shoved the original ball. As long as there was still kinetic energy in the initial ball when it hit the second ball, then the second ball will be sent away. This is somewhat still the case with regards to the photoelectric effect, but not exactly. The photoelectric effect deals mainly with light waves and electrons. The electrons are in a metal, which if you've ever opened anything electronic, you'll notice that it's filled with metal wires. That's because electrons easily move through metals, which is why metals can carry a current. This also makes the electrons easily knocked away from the metal by a source of energy like, say, light.

There's one more very important thing to consider -- at the time of this experiment, light was thought to be a wave (For some very good reasons, explained at Built on Facts). The energy transmitted from light was thought to be dependent upon a given light beams "Intensity", which was determined by the wave's Amplitude. This is important because the electrons held in the metal have 1) a certain amount of energy they need to absorb in order to knock whatever force is holding them in place away, as well as 2) however much more energy is added to the electron to get it moving. However, when Einstein flashed both bright and dim lights on his sheet of metal, there was no change in how many electrons were ejected. This means that the amount of energy from a light beam was not dependent upon its intensity. Further, there was a given Frequency where electrons were no longer ejected. So, the energy from light must be dependent upon how frequent each wave hit the metal, as opposed to how many waves hit the light in a given time. To illustrate this:

In these two drawings, the light with one "wave", but more frequency (illustrated by the shorter wave lengths, as all light travels at a constant speed) has a GREATER amount of energy than the drawing on the left with four "waves" hitting the metal plate all at the same time. Now, in everyday life, supposing you throw four balls at an equal amount of Force at a target and they all hit at the same time, you're going to transfer all of the energy in each of those those balls into the target at the same time -- which will give you a greater overall impact. If you were to throw them separately, but more frequently, the net energy transfered to the target would be the same, but the impact would be 1/4 of the initial example each time you threw the ball. In the case of the light waves, not only is the energy transfer greater with frequency, but so is the overall impact! This is completely contrary to everyday intuition (which is fine, as physical systems aren't actually supposed to do anything. we just observe what they do, then describe them). This all ALSO resulted in confirming a separate experiment by Planck that stated the same thing, but came from different angles -- which gave further support that the energy in a light wave is not dependent upon intensity, but instead on frequency. The end all equation to this all was:

E = hν

Where E is energy, h is a physical constant (called Plank's Constant), and nu (ν) is the frequency of a given wave.

Now... OK... admittedly, here's where things are still shady for myself... but the photoelectric effect also demonstrates the dual nature of light: That light exhibits both wave-like and particle-like features. The best formulation I can come up with here is that, supposing we have a wave, like above, and we know the frequency that the wave needs to be at in order to knock electrons loose (as frequency corresponds to energy). We set that frequency to just above what is required to detect electrons being knocked loose. Now, we spread that light beam out with a lens over an entire metallic surface. What is observed? Whether the light is spread out or focused on a single point, the same number of electrons are ejected. If we had a wave, the entire wave would be spread out over the surface, and we would then also have less energy transferred to the plate, and we would expect electrons to not be knocked loose. However, since we still observe electrons not only be knocked loose, but the exact same number of electrons being knocked loose, we have to conclude that light energy comes in packets. And THAT is the beginning of quantum (meaning "piece") mechanics.

Holy. Fuckin'. Shit.

(apologies for any bungling to actual history of this discovery, or even misrepresentation of the theory. Really, I'm just beginning to grapple with these concepts. Someday, this stuff'll make even more sense)